Enzyme kinetic constants in vivo are largely unknown, which limits the construction of large metabolic models. In theory, kinetic constants can be fitted to measured metabolic fluxes, metabolite concentrations, and enzyme concentrations, but these estimation problems are typically non-convex. This makes them hard to solve, especially if models are large. Here I assume that the metabolic fluxes are given and show that consistent kinetic constants, metabolite levels, and enzyme levels can then be found by solving a convex optimality problem. If logarithmic kinetic constants and metabolite concentrations are used as free variables and if Gaussian priors are employed, the posterior density is strictly convex. The resulting estimation method, called model balancing, can employ a wide range of rate laws, accounts for thermodynamic constraints on parameters, and considers the dependences between flux directions and metabolite concentrations through thermodynamic forces. It can be used to complete and adjust available data, to estimate in-vivo kinetic constants from omics data, or to construct plausible metabolic states with a predefined flux distribution. To demonstrate model balancing and to assess its practical use, I balance a model of E. coli central metabolism with artificial or experimental data. The tests show what information about kinetic constants can be extracted from omics data and reveal practical limits of estimating kinetic constants in vivo.
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